Chapter 10: t-tests

2. Chapter 10: t-tests The Two-Sample Independent & Related-Sample t-Tests

3. is the mean of the first sample • is the mean of the second sample • is the estimated population standard deviation of the first sample • is the estimated population standard deviation of the second sample • is the number of scores in the first sample • is the number of scores in the second sample New Statistical Notation

4. Understanding the Two-Sample Experiment

5. Condition 1 produces sample mean that represents • Condition 2 produces sample mean that represents Two-Sample Experiment • Participants’ scores are measured under two conditions of the independent variable

6. Two-Sample t-Test • parametric statistical procedure for determining whether the results of a two-sample experiment are significant • There are two versions of the two-sample t-test • The independent samples t-test • The related samples t-test.

7. Relationship in the Population in a Two-sample Experiment

8. The Independent Samples t-Test

9. Independent Samples t-Test • The independent samples t-test is the parametric procedure used for significance testing of two sample means from independent samples • Two samples are independent when we randomly select and assign a participant to a sample

10. Assumptions of the Independent Samples t-Test • The dependent scores measure an interval or ratio variable • The populations of raw scores form normal distributions • The populations have homogeneous variance. Homogeneity of variance means that the variance of all populations being represented are equal. • While Ns may be different, they should not be massively unequal.

11. Two-tailed test • One-tailed test • If m1 is expected to If m2 is expected to • be larger than m2 be larger than m1 Statistical Hypotheses

12. Critical Values • Critical values for the independent samples t-test (tcrit) are determined based on degrees of freedom df = (n1 - 1) + (n2 - 1), the selected a, and whether a one-tailed or two-tailed test is used

13. Sampling Distribution • The sampling distribution of differences between means is the distribution of all possible differences between two means when they are drawn from the raw score population described by H0

14. Computing the Independent Samples t-Test • Calculate the estimated population variance for each condition

15. Computing the Independent Samples t-Test • Compute the pooled variance

16. Computing the Independent Samples t-Test • Compute the standard error of the difference

17. Computing the Independent Samples t-Test • Compute tobt for two independent samples

18. Computing the Independent Samples t-Test • These steps can be combined into the following computational formula for the independent samples t-test

19. Confidence Interval • When the t-test for independent samples is significant, a confidence interval for the difference between two ms should be computed

20. Power • To maximize power in the independent samples t-test, you should maximize the difference produced by the two conditions • Minimize the variability of the raw scores • Maximize the sample ns

21. Related Samples t-Test

22. Related Samples • The related samples t-test is the parametric inferential procedure used when we have two sample means from two related samples • Related samples occur when we pair each score in one sample with a particular score in the other sample • Two types of research designs that produce related samples are matched samples design and repeated measures design

23. Matched Samples Design • In a matched samples design, the researcher matches each participant in one condition with a participant in the other condition • We do this so that we have more comparable participants in the conditions

24. Repeated Measures Design In a repeated measures design, each participant is tested under all conditions of the independent variable.

25. Assumptions of the Related Samples t-Test • The assumptions of the related samples t-test are when the dependent variable involves an interval or ratio scale • The raw score populations are at least approximately normally distributed • The populations being represented have homogeneous variance • Because related samples form pairs of scores, the n in the two samples must be equal

26. Transforming the Raw Scores • In a related samples t-test, the raw scores are transformed by finding each difference score • The difference score is the difference between the two raw scores in a pair • The symbol for a difference score is D

27. Two-tailed test • One-tailed test • If we expect the If we expect thedifference to be difference to belarger than 0 less than 0 Statistical Hypotheses

28. Estimated Population Variance of the Difference Scores • The formula for the estimated population variance of the difference scores is

29. Standard Error of the Mean Difference • The formula for the standard error of the mean difference is

30. Computing the Related Samples t-Test • The computational formula for the related samples t-test is

31. Critical Values • The critical value (tcrit) is determined based on degrees of freedom df = N - 1 • The selected a, and whether a one-tailed or two-tailed test is used

32. Confidence Interval • When the t-test for related samples is significant, a confidence interval for mD should be computed

33. Power • The related samples t-test is intrinsically more powerful than an independent samples t-test • To maximize the power you should • Maximize the differences in scores between the conditions. • Minimize the variability of the scores within each condition. • Maximize the size of N.

34. Describing the Relationship in a Two-Sample Experiment

35. Describing the Relationship • Once a t-test has been shown to be significant, the next step is to describe the relationship • In order to describe the relationship, you should • Compute a confidence interval • Graph the relationship • Compute the effect size • Compute the appropriate correlation coefficient to determine the strength of the relationship